Problem: Solve for $x$ : $ 3|x + 8| + 1 = 5|x + 8| + 7 $
Answer: Subtract $ {3|x + 8|} $ from both sides: $ \begin{eqnarray} 3|x + 8| + 1 &=& 5|x + 8| + 7 \\ \\ {- 3|x + 8|} && {- 3|x + 8|} \\ \\ 1 &=& 2|x + 8| + 7 \end{eqnarray} $ Subtract $7$ from both sides: $ \begin{eqnarray} 1 &=& 2|x + 8| + 7 \\ \\ {- 7} && {- 7} \\ \\ -6 &=& 2|x + 8| \end{eqnarray} $ Divide both sides by ${2}$ $ \dfrac{-6} {{2}} = \dfrac{2|x + 8|} {{2}} $ Simplify: $ -3 = |x + 8| $ The absolute value cannot be negative. Therefore, there is no solution.